Question

Rewrite the equation shown in slope-intercept form. Identify the slope of the equation, the x intercept and the y-intercept. Then graph the equation. Make sure to show all your work in the
spaces provided.

Answer 1

Answer:

Slope-intercept form: y = 3x + 5

Slope: 3

y-intercept: 5

Step-by-step explanation:

What is slope-intercept form?

When the equation of a line is written in the slope-intercept form, we can easily identify the slope from the coefficient of x and the y-intercept from the constant.

The slope-intercept form is expressed as y = mx + c, where m is the slope and c is the y-intercept. Note that other textbooks might use y = mx + b instead, but both have the same meaning as both m and b or c will be replaced by a certain value.

Rewriting in slope-intercept form

To rewrite and equation in the slope-intercept form, isolate the y term on the right-hand side of the equation and divide the whole equation by the coefficient of y.

Working

$y - ( - 7) = 3(x - ( - 4))$

Expand:

$y + 7 = 3(x + 4)$

$y + 7 = 3x + 12$

Subtract both sides by 7:

$y = 3x + 12 - 7$

$\bf{y = 3x + 5}$

Since the coefficient of y is already 1, we have arrived at our final answer.

Identifying slope

When the equation is in the slope-intercept form, the slope can be identified from the coefficient of x. This refers to the number that comes before x which is multiplied to x.

Thus, the slope is 3.

Identifying the y-intercept

The y-intercept is the value of the constant in the slope-intercept form. This refers to the number that is not attached to any variables.

Hence, the y-intercept is 5.

Note that the y-intercept can also be found by substituting x = 0 into the equation.

Identifying the x-intercept

The x-intercept occurs at y = 0. Since we have the equation of the line, we can substitute y = 0 into the equation to find the value of x when y = 0.

Working

y = 3x + 5

When y = 0,

0 = 3x + 5

3x = -5

Divide both sides by 3:

$x = - \frac{5}{3}$

Graphing the equation

I have attached the graph as an image. If only a sketch is required, there are 3 pieces of information that needs to be labelled on the graph:

1. Axes
2. Intercepts
3. Equation of the line

Additional resources:

To learn more about slope-intercept form, check out: https://brainly.com/question/12571101