The equation of the line that passes through the points [tex]\left( {1, - 5} \right)[/tex] and [tex]\left( {3, - 17} \right)[/tex] is [tex]\boxed{y= -6x + 1}.[/tex]
Further explanation:
The linear equation with slope m and intercept c is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left({{x_2},{y_2}}\right)[/tex] can be expressed as,
[tex]\boxed{m=\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Given:
The passes through the points are [tex]\left({1, - 5}\right)[/tex] and [tex]\left({3, - 17}\right).[/tex]
Explanation:
The line passes the points that are [tex]\left({1, - 5}\right)[/tex] and [tex]\left( {3, - 17}\right).[/tex]
The slope of the line can be obtained as follows.
[tex]\begin{aligned}m&=\frac{{-17-\left( { - 5}\right)}}{{\left( 3 \right) - 1}}\\&=\frac{{ - 12}}{2}\\&=- 6\\\end{aligned}[/tex]
The slope of the line ism = - 6.
The line passes through the point [tex]\left({3, - 17}\right).[/tex]
Substitute 3 for x, - 6 for m and -17 for y in equation y = mx + c to obtain the value of c.
[tex]\begin{aligned}-17&= - 6\left(3\right)+c\\- 17&=- 18+ c\\- 17 + 18 &= c\\1 &=c\\\end{aligned}[/tex]
The equation is y = - 6x + 1.
Hence, the equation of the line that passes through the points [tex]\left( {1, - 5}\right)[/tex] and [tex]\left( {3, - 17}\right)[/tex] is [tex]\boxed{y= -6x + 1}.[/tex]
Learn more:
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.
