A line passes through the points (-2,5) and (3,10) write its equation in slope intercept form
To find the equation of a line in slope-intercept form (y = mx + b), we need to find the values of slope (m) and y-intercept (b).
Step 1: Find the slope (m)
The formula to calculate the slope is: m = (y2 - y1) / (x2 - x1)
Using the points (-2, 5) and (3, 10), we can substitute the values into the formula:
m = (10 - 5) / (3 - (-2))
m = 5/5
m = 1
Step 2: Find the y-intercept (b)
To find the y-intercept, we can substitute one of the points (-2, 5) into the slope-intercept form (y = mx + b) and solve for b.
5 = 1*(-2) + b
5 = -2 + b
b = 5 + 2
b = 7
So the y-intercept (b) is equal to 7.
Step 3: Write the equation in slope-intercept form.
Now that we have the values of the slope (m = 1) and the y-intercept (b = 7), we can write the equation in slope-intercept form.
The equation is:
y = 1x + 7
Simplifying,
y = x + 7
Therefore, the equation of the line passing through the points (-2, 5) and (3, 10) in slope-intercept form is y = x + 7.