Writing Linear Equations in Slope-Intercept Form Practice

Question

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4 of 54 of 5 Items

Question
Use the table to answer the question.

x
y

1 −5

2 0
3 5
Write the equation of the line in slope-intercept form.

(1 point)
y=
x+
(
)

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b).

1. Calculate the slope (m) using two points from the table. We'll use the points (1, -5) and (2, 0).

The formula for slope is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (1, -5) and (2, 0):

• \( y_1 = -5 \), \( x_1 = 1 \)
• \( y_2 = 0 \), \( x_2 = 2 \)

Now substitute:

\[ m = \frac{0 - (-5)}{2 - 1} = \frac{0 + 5}{1} = \frac{5}{1} = 5 \]

2. Find the y-intercept (b). We can use one of the points and the slope to solve for b. Let's use the point (2, 0).

Using the slope-intercept form: \[ y = mx + b \] Substituting the known values:

\[ 0 = 5(2) + b \] \[ 0 = 10 + b \] \[ b = 0 - 10 = -10 \]

3. Form the equation. Now we have the slope (m = 5) and the y-intercept (b = -10). Therefore, the equation of the line in slope-intercept form is:

\[ y = 5x - 10 \]

So your answer would be:

y = 5x - 10