First we have to find the slope of the givent line and for that we use rise / run method .
The points are (-4,4),(4,-2)
Here rise is
[tex]-2-4 =-6[/tex]
And run is
[tex]4-(-4)=8[/tex]
So slope is
[tex]= \frac{-6}{8} = \frac{-3}{4}[/tex]
And the slopes of perpendicular lines are negative reciprocal of each other .
Therefore the slope of the required perpendicular line is
[tex]-(- \frac{4}{3}) = \frac{4}{3}[/tex]
Now we use slope intercept form, and put x intercept , that is (6,0) and the slope that is 4/3 ,
[tex]y=mx+b \\ 0 = \frac{4}{3}*6 +b \\ 0=8+b \\ b =-8[/tex]
Therefore required equation is
[tex]y= \frac{4}{3}x -8[/tex]
Correct option is the third option .
The equation of the line that is perpendicular to the given line and has an x-intercept of 6 is [tex]\boxed{y= \frac{4}{3}x - 8}[/tex].Option c is correct.
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 = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Given:
The options of the equation are as follows.
a.[tex]y = - \dfrac{3}{4}x + 8[/tex]
b.[tex]y =-\dfrac{3}{4}x + 6[/tex]
c.[tex]y=\dfrac{4}{3}x - 8[/tex]
d.[tex]y = \dfrac{4}{3}x - 6[/tex]
Explanation:
The x-intercept is of the perpendicular line is 6. Therefore, the point of passing is [tex]\left( {6,0}\right).[/tex]
Substitute 0 for y, 6 for x and [tex]\dfrac{4}{3}[/tex] for m in equation y = mx + c.
[tex]\begin{aligned}y&= mx + c\\0&=\frac{4}{3} \times6 + c\\0&=8 + c\\- 8&= c\\\end{aligned}[/tex]
The blue line intersect the points that are [tex]\left( {-4,4} \right) {\text{and}\left( {4,-2} \right).[/tex]
The slope of the line can be obtained as follows.
[tex]\begin{aligned}m&=\frac{{ - 2 - 4}}{{4 - \left({ - 4} \right)}}\\&=\frac{{ - 6}}{8}\\&=\frac{{ - 3}}{4}\\\end{aligned}[/tex]
The slope of the line is [tex]m = - \dfrac{3}{4}.[/tex]
The slope of the perpendicular line is the negative reciprocal of the slope of the line.
[tex]\begin{aligned}{m_1}&= - \frac{1}{m}\\&=\frac{4}{3}\\\end{aligned}[/tex]
The equation of the line that is perpendicular to the given line and has an x-intercept of 6 is [tex]\boxed{y= \frac{4}{3}x - 8}.[/tex]
Option (a) is not correct as it satisfy the equation of the graph.
Option (b) is not correct as it satisfy the equation of the graph.
Option (c) is correct as it satisfy the equation of the graph.
Option (d) is not correct as it satisfy the equation of the graph.
Hence,[tex]\boxed{{\text{Option (c)}}}[/tex] is correct.
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear inequalities
Keywords: numbers, slope, slope intercept, inequality, equation, linear equation, shaded region, y-intercept, graph, representation, origin, perpendicular, x-intercept 6.
