How Do You Write A Linear Equation Given Slope & A Point?
Linear equations are given in the form y = ax + b with known coefficients a and b. Linear equation graphs are straight lines having two characteristics. One of them is the plot slope that is numerically equal to the coefficient a. The other one is a y-intercept that is the y-coordinate of the point where the plot crosses the y-axis and equals the coefficient b. However, a linear equation can be unambiguously defined in several other ways. As an example, consider how to write a linear equation if its plot with the slope 4 passes through the point having the following coordinates: x1 = 3 and y1 = 5. Write the linear equation for the point with the coordinates x1 and y1: y1 = ax1 + b In our example, it would be: 5 = 3a + b Subtract the equation obtained in Step 1 from the generic equation form y = ax + b: y = ax + b y1 = ax1 + b ——————- y – y1 = ax – ax1 Remembering that the coefficient a is the plot slope, you can write the equation in the slope-point form: y – y1 = slope * (
