Find the equation of the line that passes through the point (2, -3) and has a sl

Find the equation of the line that passes through the point (2, -3) and has a slope of 4.

Find the equation of the line that passes through the point (2, -3) and has a slope of 4.

Step 1: Identify the point and slope. The point is (2, -3) and the slope is 4.
Step 2: Use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.
Step 3: Substitute the values into the point-slope form. Here, x1 = 2, y1 = -3, and m = 4. So, it becomes y - (-3) = 4(x - 2).
Step 4: Simplify the equation. This gives us y + 3 = 4(x - 2).
Step 5: Distribute the 4 on the right side: y + 3 = 4x - 8.
Step 6: Isolate y by subtracting 3 from both sides: y = 4x - 8 - 3.
Step 7: Combine the constants on the right side: y = 4x - 11.

Point-Slope Form – The equation of a line in point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Slope-Intercept Form – The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.