It doesn\u2019t have a definite length and has zero width.<\/span><\/p>\n Every straight line can be expressed in the form of a linear equation (ax + by = c) and if there is any point satisfying that equation, then it lies on that line.<\/span><\/p>\n Every point on the straight line have two parts:<\/span><\/span><\/p>\n <\/p>\n The angle between the line and the positive x-axis is known as the inclination of the line. It can be positive or negative based on the direction of measurement.\u00a0<\/span><\/p>\n <\/span><\/p>\n <\/p>\n The slope of a line is defined as the measure of the steepness of the same line. It is the tangent of the inclination angle of that line. It can be also referred to as the ratio of the difference between the ordinates to the difference between the abscissa of any two points on the line.<\/span><\/p>\n <\/span><\/p>\n \\text { Slope }=\\frac{\\text { Difference between ordinates (y coordinates) }}{\\text { Difference between abscissa ( } x \\text { coordinates) }}<\/span><\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n <\/span><\/p>\n A line is passing through points point P and Q having coordinates \\left(x_{1}, y_{1}\\right) \\text { and }\\left(x_{2}, y_{2}\\right)<\/span><\/span>respectively\u00a0<\/span><\/p>\n The slope of \\mathrm{PQ}=\\mathrm{m}=\\tan \\theta=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}<\/span><\/span><\/p>\n <\/span><\/p>\n When a line is parallel to another line, then their slopes are equal to each other\u00a0<\/span><\/p>\n m_{1}=m_{2}<\/span><\/span><\/p>\n <\/span><\/p>\n When a line is perpendicular to another line, the product of their respective slopes is equal to (-1).<\/span><\/p>\n Let there be a line containing points P\\left(x_{1}, y_{1}\\right)\\text{ and } Q\\left(x_{2}, y_{2}\\right)<\/span><\/span>and the other line contains points A\\left(x_{3}, y_{3}\\right)\\text{ and } B\\left(x_{4}, y_{4}\\right)<\/span>.<\/span><\/p>\n\\text { The slope of } \\mathrm{PQ}=\\mathrm{m}_{1}=\\frac{y_{1}-y_{2}}{x_{1}-x_{2}}<\/span>\n\\text { The slope of } \\mathrm{AB}=\\mathrm{m}_{2}=\\frac{y_{3}-y_{4}}{x_{3}-x_{4}}<\/span>\n If PQ is perpendicular to AB:<\/span><\/p>\n \\Rightarrow \\mathrm{m}_{1} \\times \\mathrm{m}_{2}=(-1) <\/span> <\/p>\n Let there be 3 points P\\left(x_{1}, y_{1}\\right), Q\\left(x_{2}, y_{2}\\right), R\\left(x_{3}, y_{3}\\right)<\/span><\/span><\/b><\/p>\n P, Q and R will be collinear when the slope of the line segment PQ will be equal to the slope of the line segment QR.<\/span><\/p>\n \\frac{y_{1}-y_{2}}{x_{1}-x_{2}}=\\frac{y_{2}-y_{3}}{x_{2}-x_{3}}<\/span><\/span><\/p>\n <\/p>\n When a line intersects with the x-axis, the distance between the origin and the point of intersection is known as the x-intercept.<\/span><\/p>\n When a line intersects with the y-axis, the distance between the origin and the point of intersection is known as the y-intercept.<\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n A line is passing through a point having coordinates \\left(x_{1}, y_{1}\\right)<\/span> <\/span>and its slope is \u2018m\u2019<\/span><\/p>\n Equation:\u00a0<\/span><\/p>\n y-y_{1}=m\\left(x-x_{1}\\right)<\/span><\/span><\/p>\n <\/span><\/p>\n A line having y-intercept equal to \u2018c\u2019 and slope equal to \u201cm\u201d<\/span><\/p>\n Equation:<\/span><\/p>\n y=m x+c<\/span><\/span><\/p>\n <\/span><\/p>\n A line is passing through two points having coordinates \\left(x_{1}, y_{1}\\right) \\text { and }\\left(x_{2}, y_{2}\\right)<\/span><\/span><\/p>\n Equation:<\/span><\/p>\n y-y_{1}=\\frac{y_{1}-y_{2}}{x_{1}-x_{2}}\\left(x-x_{1}\\right)<\/span><\/span><\/p>\n <\/span><\/p>\n A line having x-intercept and y-intercept equal to \u2018a\u2019 and \u2018b\u2019 respectively.<\/span><\/p>\n \\frac{x}{a}+\\frac{y}{b}=1<\/span><\/span><\/p>\n This line also passes through the point (0,b) and (a,0).<\/span><\/p>\n <\/span><\/p>\n 1. The x coordinate of a point on the line (y = 2x + 3) is 3. Find its y coordinate.<\/b><\/p>\n We know that every point present on the line satisfies its equation.<\/span><\/p>\n x coordinate of the point = 3<\/span><\/p>\n For finding y-coordinate, we have to put the value of x in the given equation<\/span><\/p>\n Equation of the line <\/span> \u21d2 y = 2<\/span>3 + 3 = 6 + 3 = 9<\/span><\/p>\n Hence the y coordinate of the point is 9.<\/span><\/p>\n <\/span><\/p>\n 2. A straight line is having a slope equal to 2. Find the slope of the line perpendicular to the given line.<\/b><\/p>\n When a line is perpendicular to another line, the product of their respective slopes is equal to (-1).<\/span><\/p>\n \\Rightarrow m_{1} \\times m_{2}=(-1) <\/span> <\/p>\n 3. The equation of a line BC is 4x + 7 = 9. Find the value of its slope (m) and y-intercept (c)<\/b><\/p>\n We have to write the given equation in slope-intercept form to find the value of \u2018m\u2019 and \u2018c\u2019.<\/span><\/p>\n \u00a0 \u00a0 \u00a0 4 x+7=9 <\/span> <\/p>\n \\text { Hence the slope is equal to } \\frac{7}{4} \\text { and the } y \\text {-intercept is equal to } \\frac{9}{4}<\/span>.<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n\n
The inclination of a straight line<\/b><\/h2>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/fhffh-300x88.png\")
<\/span><\/p>\n<\/b><\/h3>\n
Important Points<\/b><\/h3>\n
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The slope of a line<\/b><\/h2>\n
Example<\/b><\/h3>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Straight-lines-01-300x266.png\")
<\/b><\/p>\nImportant Points<\/b><\/h3>\n
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Parallel lines<\/b><\/h2>\n
Perpendicular lines<\/b><\/h2>\n
\\Rightarrow \\frac{y_{1}-y_{2}}{x_{1}-x_{2}} \\times \\frac{y_{3}-y_{4}}{x_{3}-x_{4}}=(-1)<\/span>
<\/span><\/p>\nCollinearity of three points<\/b><\/h2>\n
X- Intercepts & Y- Intercepts<\/b><\/h2>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Straight-lines-02-300x199.png\")
<\/span><\/p>\n<\/b><\/h2>\n
Equation of a straight line\u00a0<\/b><\/h2>\n
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Solved Examples<\/b><\/h2>\n
<\/span>y = 2x + 3<\/span><\/p>\n
\\Rightarrow 2 \\times m_{2}=(-1) <\/span>
\\Rightarrow m_{2}=(-1 \/ 2)<\/span><\/span><\/p>\n
\\Rightarrow\u00a0 \\frac{4 x}{4}+\\frac{7}{4}=\\frac{8}{4} <\/span>
\\Rightarrow\u00a0 x+\\frac{7}{4}=\\frac{9}{4} <\/span>
\\Rightarrow\u00a0 m=\\frac{7}{4} \\text { and } c=\\frac{9}{4}<\/span><\/span><\/p>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n