Write the equation in slope-intercept form of the line that passes through the point (-3, 5) and has a slope of 2/3.
you have a point and a slope, so start with that form:
y-5 = (2/3)(x+3)
Now just rearrange things to wind up with the slope-intercept form.
y-5 = (2/3)x + 2
...
To write the equation of a line in slope-intercept form, we need the slope of the line and a point that lies on the line. In this case, the slope is given as 2/3, and the point (-3, 5) lies on the line.
The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
First, we can plug in the given slope into the equation:
y = (2/3)x + b
Next, we substitute the coordinates of the given point (-3, 5) into the equation. This will allow us to solve for the y-intercept, b.
5 = (2/3)(-3) + b
Now, we simplify the equation:
5 = -2 + b
To isolate b, we can add 2 to both sides of the equation:
5 + 2 = b
b = 7
With the value of b, we have the complete equation in slope-intercept form:
y = (2/3)x + 7