Step-by-step explanation:
To determine the equation of the line parallel to [tex]5x + 2y = 12[/tex], we need to first determine the slope of the given line.
A line in slope-intercept form is represented by the following:
[tex]y = mx + b[/tex]
where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the y-intercept.
Rearranging the given line will give us the slope of the line:
[tex]5x + 2y = 12[/tex]
[tex]2y = -5x + 12[/tex]
[tex]y = -\frac{5}{2}x + 6[/tex]
From this, since we know the lines are parallel, if the slope of the given line is [tex]-\frac{5}{2}[/tex], then the slope of the line we are constructing must also be [tex]-\frac{5}{2}[/tex].
We can now start to construct the line with the same slope-intercept form:
[tex]y = mx + b[/tex]
[tex]y = -\frac{5}{2}x + b[/tex]
To determine the y-intercept, [tex]b[/tex], we can plug in the point [tex](-2, 4)[/tex] since we are told from the problem statement that this parallel line runs through it:
[tex]y = -\frac{5}{2}x + b[/tex]
[tex]4 = -\frac{5}{2}(-2) + b[/tex]
[tex]4 = 5 + b[/tex]
[tex]b = -1[/tex]
Finally, we have our parallel line:
[tex]y = -\frac{5}{2}x - 1[/tex]
If this line needs to be in standard form, we can rearrange it a little:
[tex]2y = -5x - 2[/tex]
[tex]5x + 2y = -2[/tex]
