Questions: Write the equation of this line in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

$Write the equation of this line in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.$

Transcript text: Write the equation of this line in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

Solution

Solution Steps

Step 1: Find the y-intercept

The y-intercept is the point where the line crosses the y-axis. In this graph, the line crosses the y-axis at the point (0, 6). Therefore, the y-intercept is 6.

Step 2: Find the slope

The slope of a line is the change in y divided by the change in x. We can pick two points on the line to calculate the slope. We already have (0, 6). Another point on the line is (1, -1).

The slope is calculated as follows: (y₂ - y₁) / (x₂ - x₁) = (-1 - 6) / (1 - 0) = -7/1 = -7

Step 3: Write the equation

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope (m) is -7 and the y-intercept (b) is 6.

Therefore, the equation of the line is y = -7x + 6.