Question

What is the Y-Int, Slope, and Slope-Intercept form?

Answer 1

Answer:

Slope = $\mathsf{\frac{3}{2}}$

Y-intercept: (0, -3)

Slope-intercept form:  $\mathsf{y\:=\frac{3}{2}x\: -\: 3}$

Step-by-step explanation:

Before identifying the values of the y-intercept, slope, and the linear equation in slope-intercept form, it is necessary to define the first two terms.

Definition of Terms:

The slope ( m ) of the equation is a ratio that compares the change in y-values (the rise) to the change in x-values (the run). Thus, it is often used as a means of measuring the steepness of a line.

The y-intercept ( b ) is the point on the graph where the line crosses the y-axis. The y-intercept is the y-coordinate of the point (0, b ), where the value of x = 0.  

Solution:

Slope

In order to solve for the slope, we must choose two points on the graph, (2, 0) and (0, -3).

Let (x₁, y₁) = (2, 0)

     (x₂, y₂) = (0, -3)

Substitute these values into the following slope formula:

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

$\mathsf{slope\: (m)\:=\:\frac{-3\:-\:0}{0\:-\:2}\:=\: \frac{-3}{-2}\:=\:\frac{3}{2}}$

Therefore, the slope of the line is:  $\mathsf{m\:=\frac{3}{2}}$.

Y-intercept:

Using the slope, $\mathsf{m\:=\frac{3}{2}}$, and one of the points from the graph, (2, 0), substitute these values into the slope-intercept form: y = mx + b:

y = mx + b

$\mathsf{0\:=\:(-\frac{3}{2})(2)\:+\:b}$

0 = 3 + b

Subtract 3 from both sides of the equation:    

0 - 3 = 3 - 3 + b

-3 = b

Therefore, the y-intercept is (0, -3), where b = -3.  

Slope-intercept form:

Given the slope, $\mathsf{m\:=\frac{3}{2}}$, and the y-intercept, b = -3, the equation of the line in slope-intercept form is:  $\mathsf{y\:=\frac{3}{2}x\: -\: 3}$.