Question
A line passes through the points \( (-5,5) \) and \( (7,-5) \). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
Ask by Valdez May. in the United States
Feb 07,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the line in slope-intercept form is \( y = -\frac{5}{6}x + \frac{5}{6} \).
Solution
To find the equation of the line in slope-intercept form (y = mx + b), follow these steps:
Step 1. Calculate the slope (m) using the two points (-5, 5) and (7, -5). The formula for the slope is:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging in the coordinates:
m = (-5 - 5) / (7 - (-5)) = (-10) / (12) = -5/6
Step 2. Use the point-slope form of the equation:
y - y₁ = m(x - x₁)
You can choose either point; using (-5, 5):
y - 5 = (-5/6)(x - (-5)) = (-5/6)(x + 5)
Step 3. Solve for y to get the equation in slope-intercept form:
y = (-5/6)(x + 5) + 5
Expand and simplify:
y = (-5/6)x - (25/6) + 5
Convert 5 to a fraction with denominator 6:
5 = 30/6
Thus:
y = (-5/6)x - 25/6 + 30/6
Simplify the constant terms:
y = (-5/6)x + 5/6
The equation of the line in slope-intercept form is:
y = (-5/6)x + 5/6
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the equation of the line in slope-intercept form \(y = mx + b\), we start by calculating the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Using the points \( (-5, 5) \) and \( (7, -5) \): \[ m = \frac{-5 - 5}{7 - (-5)} = \frac{-10}{12} = -\frac{5}{6} \] Next, we can use the slope and one of the points to find the y-intercept \(b\). Let’s use the point \( (-5, 5) \): \[ 5 = -\frac{5}{6}(-5) + b \] \[ 5 = \frac{25}{6} + b \] \[ b = 5 - \frac{25}{6} = \frac{30}{6} - \frac{25}{6} = \frac{5}{6} \] Now, putting it all together, the slope-intercept form of the line is: \[ y = -\frac{5}{6}x + \frac{5}{6} \]
