write the slope-intercept form of the equation of the line that satisfies the given conditions. passes though (5,1) m=3/2
To find the slope-intercept form of the equation of a line, we need two pieces of information: the slope (m) and a point on the line (x, y). In this case, we are given that the line passes through the point (5, 1) and has a slope of m = 3/2.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Substitute the given values into the equation.
m = 3/2
x = 5
y = 1
Step 2: Substitute the values into the equation y = mx + b and solve for b.
1 = (3/2)(5) + b
1 = 15/2 + b
To isolate b, we subtract 15/2 from both sides of the equation:
b = 1 - 15/2
b = 2/2 - 15/2
b = -13/2
Now we have the slope (m = 3/2) and the y-intercept (b = -13/2). We can plug these values into the slope-intercept form of the equation to get the final result:
y = (3/2)x - 13/2
So, the slope-intercept form of the equation of the line that passes through the point (5, 1) with a slope of 3/2 is y = (3/2)x - 13/2.
so, starting with the point-slope form, you get
y-1 = 3/2 (x-5)
Now just rearrange the terms to get y = mx+b