Answer: To write the equation of the line that is parallel to the graph of y = x – 4 and passes through the point (-2, 3), we can use the fact that parallel lines have the same slope.
The slope of y = x – 4 is 1, since the coefficient of x is 1.
So, we can write the equation of the line in the slope-intercept form y = mx + b, where m = 1 and b is the y-intercept. To find the y-intercept, we can substitute the point (-2, 3) into the equation:
y = 1x + b
3 = 1(-2) + b
3 = -2 + b
b = 5
so the equation of the line in slope-intercept form is y = 1x + 5
To write the equation of the line that is parallel to the graph of y + 2x = 4 and passes through the point (-1, 2), we can use the fact that parallel lines have the same slope.
The slope of the equation y + 2x = 4 is -1/2, since the coefficient of x is -1/2.
So, we can write the equation of the line in the slope-intercept form y = mx + b, where m = -1/2 and b is the y-intercept. To find the y-intercept, we can substitute the point (-1, 2) into the equation:
y = -1/2 x + b
2 = -1/2(-1) + b
2 = -1/2 + b
b = 5/2
so the equation of the line in slope-intercept form is y = -1/2x + 5/2
It's important to note that the slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is the point where the line crosses the y-axis.