Q26. - Algebra 2

Question

Write an equation in slope-intercept form for the line that satisfies each set of conditions

$\text{ Slope -5, }y-\text{intercept 11}$

Step-by-Step Solution

Answer

The equation of the line in slope intercept having slope as -5 and y-intercept as 11 is $y=-5x+11$.

Step-1 – Apply the concept of slope-intercept form of a linear equation

The slope of a line is the ratio of the change in the y-coordinates to the change in the x- coordinates.

The slope-intercept form of the equation of a line is given by $y=mx+b$where m is the slope and b is the y-intercept.

Step-2 – Substitute the value of slope

The given slope is -5. Hence substitute m in the equation $y=mx+b$ by -5.

Therefore, the slope intercept form of a linear equation becomes 

$\begin{array}{c}y=(-5)x+b\\ y=-5x+b-----\left(1\right)\end{array}$

Step-3 – Substitute the value of y -intercept

Given that the y-intercept is 11. Hence take the value of b as 11 in the slope intercept form of a linear equation.

Therefore, from equation (1) obtained in step 2, the slope intercept form is obtained as

$\begin{array}{r}y=-5x+b\\ \Rightarrow y=-5x+11\end{array}$