The equation of the line in standard form passing through the point (-4 , 2) with slope equal to 3 is 3x - y = -14.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values of the slope and the point to set up the equation.
(y - y1) = m(x - x1)
where m = 3 and (x1 , y1) = (-4 , 2)
(y - 2) = 3(x - -4)
y - 2 = 3(x + 4)
y - 2 = 3x + 12
To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.
y - 2 = 3x + 12
3x - y = -2 -12
3x - y = -14
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