Question
Draw the graph of linear function y=2x+3
Find the equation of the line passing through point (3,5) with slope 2
Find the equation of the line passing through point (3,5) with slope 2
Answers
GPT 3.5
To draw the graph of the linear function y = 2x + 3, we can start by finding two points on the graph. One way to find these points is to let x = 0 and x = 1, and then find the corresponding y values.
When x = 0, y = 2(0) + 3 = 3. So one point on the graph is (0, 3).
When x = 1, y = 2(1) + 3 = 5. The second point is (1, 5).
Plotting these two points and drawing a straight line through them, we can graph the linear function y = 2x + 3.
Now, to find the equation of the line passing through point (3,5) with slope 2, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values x1 = 3, y1 = 5, and m = 2, we get:
y - 5 = 2(x - 3)
y - 5 = 2x - 6
y = 2x - 1
So, the equation of the line passing through point (3,5) with slope 2 is y = 2x - 1.
When x = 0, y = 2(0) + 3 = 3. So one point on the graph is (0, 3).
When x = 1, y = 2(1) + 3 = 5. The second point is (1, 5).
Plotting these two points and drawing a straight line through them, we can graph the linear function y = 2x + 3.
Now, to find the equation of the line passing through point (3,5) with slope 2, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values x1 = 3, y1 = 5, and m = 2, we get:
y - 5 = 2(x - 3)
y - 5 = 2x - 6
y = 2x - 1
So, the equation of the line passing through point (3,5) with slope 2 is y = 2x - 1.