Write the point-slope from of the line’s equation satisfying the given conditions. Then use the point-slope from of the equation to write the slope-intercept from of the equation.
Slope = 6, passing through (2,5)
The point-slope from of the equation of a nonvertical line with slope m that passes through the point (x1,y1) is y –y1 = m (x – x1).
In this problem , m = 6, x1 = 2, and y1 = 5.
Write the point-slope form of the line satisfying the conditions.
y –y1 = m (x – x1)
y – 5 = 6(x -2)
The point-slope from of the equation of the line is y – 5 = 6(x -2). Solve this equation for y and write an equivalent equation in slope- intercept form (y = mx +b).
y – 5 = 6 (x-2)
y – 5 = 6x – 12
y = 6x – 7
Therefore, the slope-intercept form of the line’s equation is y = 6x – 7.