What is the equation of this line in slope-intercept form?

Question

Responses

y=3x−2
y equals 3 x minus 2

y=−13x+2
y equals negative 1 third x plus 2

y=−3x+2
y equals negative 3 x plus 2

y = 3x + 2
y = 3 x + 2
Number graph ranging from negative 5 to 5 on the x and y axes. A line is drawn on the graph that passes through the labeled points begin ordered pair negative 1 comma 5 end ordered pair and begin ordered pair 1 comma negative 1 end ordered pair

Answer 1

To find the equation of the line that passes through the points (-1, 5) and (1, -1), we can follow these steps:

1. Calculate the slope (m) of the line using the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (-1, 5) and (1, -1): \[ m = \frac{-1 - 5}{1 - (-1)} = \frac{-6}{2} = -3 \]

2. Use the point-slope form of a line to find the equation. The point-slope form is: \[ y - y_1 = m(x - x_1) \] We can use one of the points, such as (-1, 5): \[ y - 5 = -3(x - (-1)) \] \[ y - 5 = -3(x + 1) \]

3. Distribute and simplify the equation: \[ y - 5 = -3x - 3 \] \[ y = -3x + 2 \]

Now the equation is in slope-intercept form, which is \(y = mx + b\). Thus, the line's equation is:

y = -3x + 2

So the correct response from your options is:

• \(y = -3x + 2\)
• \(y\) equals negative \(3\) times \(x\) plus \(2\).