Show & explain the steps for using Point-Slope Form to write the equation of the given line in Slope-intercept form
Given: A line with a slope of -3/7 that passes through the point (7,-5)
To write the equation of the given line in slope-intercept form, we need to use the point-slope form and then convert it to slope-intercept form. Here are the steps to follow:
Step 1: Understand the Point-Slope Form
The point-slope form of a linear equation is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
Step 2: Identify the Given Information
In the given problem, we are given the slope of the line, which is -3/7, and a point on the line, which is (7, -5).
Step 3: Plug in the Values
Substitute the values of the given slope and point into the point-slope form.
y - (-5) = (-3/7)(x - 7)
Step 4: Simplify the Equation
Let's simplify the equation step-by-step.
First, simplify the negative sign:
y + 5 = (-3/7)(x - 7)
Distribute the slope (-3/7) to the terms inside the parentheses:
y + 5 = (-3/7)x + 3
Step 5: Rearrange the Equation
To write the equation in slope-intercept form (y = mx + b), we need to isolate the y-term on one side. Rearrange the equation by moving the 5 to the other side:
y = (-3/7)x + 3 - 5
Combine like terms:
y = (-3/7)x - 2
Step 6: Finalize the Equation
The equation of the line in slope-intercept form is:
y = (-3/7)x - 2
That's it! You have successfully written the equation of the given line in slope-intercept form.