Write the equation of the line through the points (1, -1) and (3, 5).
Get the complete, step-by-step math solution for: "Write the equation of the line through the points (1, -1) and (3, 5).". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Calculate the slope
The slope m of a line passing through two points (x1,y1) and (x2,y2) is given by the formula for the change in y divided by the change in x. We will use the given points (1,−1) and (3,5) to calculate the slope.
Step 2: Substitute coordinates to find slope
Substitute the coordinates of the given points (x1,y1)=(1,−1) and (x2,y2)=(3,5) into the slope formula. This gives us a slope of 3.
Step 3: Use the point-slope form
Now that we have the slope, we can use the point-slope form of a linear equation. This form requires the slope m and one point (x1,y1) on the line.
Step 4: Substitute slope and a point
Substitute the calculated slope m=3 and one of the given points, for example (1,−1), into the point-slope form. This will allow us to simplify the equation into the standard slope-intercept form.
Step 5: Simplify to slope-intercept form
Simplify the equation by distributing the slope and isolating y to get the equation in the slope-intercept form, y=mx+c.