Question

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(-3,3), m=4$$

Short answer

The equation of the line in standard form that passes through the point (-3,3) and has a slope of 4 is \(4x - y = -15\).

Step-by-step solution

Use the slope-intercept form

We use the slope-intercept form of the line equation which is \(y = mx + b\), where \(m = 4\) is the slope and \((-3, 3)\) is the point that the line passes through. Substitute these values in to get the equation: \(3 = 4*(-3) + b\). From here, we solve for \(b\).

Solve for the y-intercept

After substitution, the equation becomes \(3 = -12 + b\). Solve this to find \(b\) which gives us \(b = 15\).

Write the equation of the line in slope-intercept form

Now that we have the slope (m = 4) and the y-intercept (b = 15), we can write the equation of the line in slope-intercept form: \(y = 4x + 15\).

Convert into standard form

The last step is to convert the slope-intercept form to standard form. The standard form is defined as \(Ax + By = C\). Let's transform our equation \(y - 4x = 15\). However, it's common to leave standard form with \(A\) as a positive integer, so we multiply the entire equation by -1, which gives us \(4x - y = -15\).