Final answer:
The slope-intercept form of the equation of a line parallel to y = -2x + 4 that passes through the point (4, 3) is y = -2x + 11.
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To find the equation of the line that is parallel to y = -2x + 4, we need to find the slope of the given line. Since the line is parallel, it will have the same slope. Therefore, the slope is -2.
Now we can use the point-slope form of a linear equation to determine the equation of the line passing through the point (4, 3) with slope -2:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 3 = -2(x - 4)
y - 3 = -2x + 8
y = -2x + 8 + 3
y = -2x + 11
Therefore, the equation of the line that passes through the point (4, 3) and is parallel to y = -2x + 4 is y = -2x + 11.