Final answer:
To find the equation for the line parallel to 2x+y-13=0 and passing through (7,-9), we need to determine the slope of the given line. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. By comparing the equation of the given line to the standard slope-intercept form, we can determine the slope. Since parallel lines have the same slope, the equation for the line passing through (7,-9) can be written using the point-slope form. The equation for the line parallel to 2x+y-13=0 and passing through (7,-9) is y = -2x + 5. To find the equation for the line with x-intercept 4 and y-intercept 2, we can use the two intercepts to determine two points on the line. Using these two points, we can find the slope of the line and write the equation using the point-slope form. The equation for the line with x-intercept 4 and y-intercept 2 is y = -1/2x + 2.
Step-by-step explanation:
In order to find the equation for the line passing through the point (7,-9) and parallel to the line 2x+y-13=0, we need to determine the slope of the given line. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. Since the given line is in the form 2x+y-13=0, we need to rearrange it into slope-intercept form.
2x + y = 13
y = -2x + 13
By comparing the equation y = -2x + 13 to the standard slope-intercept form, we can see that the slope of the given line is -2. Since parallel lines have the same slope, the slope of the line passing through (7,-9) will also be -2. Using the point-slope form of a linear equation, the equation for the line parallel to 2x+y-13=0 and passing through (7,-9) can be written as:
y + 9 = -2(x - 7)
y + 9 = -2x + 14
y = -2x + 5
Therefore, the equation for the line parallel to 2x+y-13=0 and passing through (7,-9) is y = -2x + 5.
To find the equation for the line with x-intercept 4 and y-intercept 2, we can use the two intercepts to determine two points on the line. The x-intercept occurs when y = 0, so we have the point (4,0). The y-intercept occurs when x = 0, so we have the point (0,2). Using these two points, we can find the slope of the line.
Slope = (change in y) / (change in x) = (0 - 2) / (4 - 0) = -2 / 4 = -1/2
Using the point-slope form, we can write the equation for the line passing through (4,0) and (0,2) as:
y - 0 = -1/2(x - 4)
y = -1/2x + 2
Therefore, the equation for the line with x-intercept 4 and y-intercept 2 is y = -1/2x + 2.