y-intercept is -3 and passing through (3,-7) what is the equation?
start with
y = mx + b
you know b = -3, it is given
so y = mx -3
you also are given the point (3,-7), so
-7 = 3m - 3
3m = -4
m = -4/3
y = (-4/3)x - 3
Thank you for explaining!
y-intercept is -3 and passing through (3,-7) what is the equation
You now have two points on the line: (0,-3) and (3,-7)
so, the slope is -4/3
Now you have a point and a slope, so using the point-slope form of the line,
y+3 = -4/3 (x-0)
as above
To find the equation of a line, we'll use the point-slope form of the equation:
y - y1 = m(x - x1)
where (x1, y1) is a point that the line passes through, and m is the slope of the line.
In this case, we are given two pieces of information:
1. The y-intercept is -3, which means that the line crosses the y-axis at y = -3. This gives us the point (0, -3).
2. The line passes through the point (3, -7).
Let's find the slope first using the two given points:
slope (m) = (y2 - y1) / (x2 - x1)
= (-7 - (-3)) / (3 - 0)
= (-7 + 3) / (3)
= -4 / 3
Now that we have the slope, we can choose either of the two given points, (0, -3) or (3, -7), to write the equation using the point-slope form. Let's choose (0, -3):
y - y1 = m(x - x1)
y - (-3) = (-4/3)(x - 0)
y + 3 = (-4/3)x
Now let's simplify the equation:
y + 3 = (-4/3)x
y = (-4/3)x - 3
Therefore, the equation of the line passing through the point (3, -7) and with a y-intercept of -3 is y = (-4/3)x - 3.