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Write the equation of the line shown in the graph in slope-intercept form.

A coordinate plane going from negative 10 to 10 in increments of 1 labeled every 5 units on the x- and y-axes.
a line runs straight through the graph from the lower left quad to the upper right quad. there are two marked spaces that the line runs through: -4, -5 and 4, 5

(1 point)
The equation in slope-intercept form is $$
.

1 answer

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

Given two points on the line:

  • Point 1: (-4, -5)
  • Point 2: (4, 5)

Step 1: Calculate the slope (m)

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting in the points:

\[ m = \frac{5 - (-5)}{4 - (-4)} = \frac{5 + 5}{4 + 4} = \frac{10}{8} = \frac{5}{4} \]

Step 2: Use one of the points to find the y-intercept (b)

We can use the point (4, 5). We can substitute \( x = 4 \), \( y = 5 \), and \( m = \frac{5}{4} \) into the slope-intercept form to find \( b \):

\[ y = mx + b \] \[ 5 = \frac{5}{4}(4) + b \] \[ 5 = 5 + b \] \[ b = 5 - 5 = 0 \]

Step 3: Write the equation in slope-intercept form

Now we have the slope \( m = \frac{5}{4} \) and the y-intercept \( b = 0 \). Thus, the equation of the line is:

\[ y = \frac{5}{4}x + 0 \quad \text{or simply} \quad y = \frac{5}{4}x \]

So, the equation in slope-intercept form is:

\[ \boxed{y = \frac{5}{4}x} \]