Write the slope-intercept form of the equation of the line parallel to y = 5x + 2 which passes through the point (4, 9)
To find the slope-intercept form of the equation of a line parallel to y = 5x + 2, we need to determine the slope of the given line, and then use that slope along with the coordinates of the given point to find the equation.
The slope-intercept form of a linear equation is given by y = mx + b, where "m" is the slope of the line and "b" is the y-intercept.
Let's find the slope of the given line y = 5x + 2. In this case, we can see that the coefficient of x is 5, so the slope of the line is 5.
Now that we know the slope is 5, we can use this slope along with the coordinates of the given point (4, 9) to find the equation of the line.
Using the point-slope formula (y - y1) = m(x - x1), where (x1, y1) are the coordinates of the given point and "m" is the slope, we can substitute the values:
(y - 9) = 5(x - 4)
Now, let's simplify this equation:
y - 9 = 5x - 20
To get the equation in slope-intercept form, we isolate the y-term:
y = 5x - 20 + 9
y = 5x - 11
Therefore, the slope-intercept form of the equation of the line parallel to y = 5x + 2 and passing through the point (4, 9) is y = 5x - 11.