Question

Need help pre college

Answer 1

Answer:

$\LARGE\mathsf{y\:=\:-\frac{7}{10}x\:-\frac{21}{10} }$

Step-by-step explanation:

Given the two points, (-3, 0) and (7, -7):

We can use these points to solve for the slope, and determine the value of the y-intercept.

Slope:

Let (x₁, y₁) = (-3, 0)

     (x₂, y₂) = (7, -7)

Substitute these values into the following slope formula:

$\large\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}$

$\large\mathsf{m = \frac {-7\: -\:0}{7\: -\:(-3)}\:=\:\frac{-7}{7\:+\:3}\:=\frac{-7}{10}}$

Therefore, the slope of the line is:  $\large\mathsf{m\:=-\frac{7}{10}}$.

Y-intercept:

Next, we must determine the value of the y-intercept. The y-intercept is the point on the graph where it crosses the y-axis. The coordinates of the y-intercept is often represented by (0, b ), where the y-coordinate, b, is used as the value of the y-intercept on the slope-intercept form.  

Using the slope,  $\large\mathsf{m\:=-\frac{7}{10}}$ , and one of the given points, (-3, 0), substitute these values into the slope-intercept form, y = mx + b, and solve for the value of b:

y = mx + b

$\large\mathsf{0\:=-\frac{7}{10}(-3)\:+\:b}$

$\large\mathsf{0\:=\frac{21}{10}+\:b}$

Subtract  $\mathsf{\frac{21}{10}}$ from both sides to isolate b :

$\large\mathsf{0\:-\frac{21}{10}\:=\frac{21}{10}\:-\:\frac{21}{10}+\:b}$

$\large\mathsf{\:-\frac{21}{10}\:=\:b}$

Therefore, the value of the y-intercept is: $\large\mathsf{b\:=\:-\frac{21}{10}}$.

Linear Equation in Slope-intercept Form:

The linear equation in slope-intercept form is:  $\LARGE\mathsf{y\:=\:-\frac{7}{10}x\:-\frac{21}{10} }$.