Final answer:
To write the slope-intercept form of a line with slope m=4 and point (2,3), substitute the values into y = mx + b to find b and rewrite the equation as y = 4x - 5.
Step-by-step explanation:
To write the slope-intercept form of a line with the given slope m=4 and passing through the point (2,3), we use the formula y = mx + b. Here, m represents the slope, and b represents the y-intercept, the point where the line crosses the y-axis. Knowing that our slope is 4 and our line passes through the point (2, 3), we can plug in the values to solve for b.
Start with the slope-intercept formula and plug in the known values:
3 = (4)(2) + b
Then solve for b:
3 = 8 + b
b = 3 - 8
b = -5
Now that we have the value for b, the slope-intercept form of our line is:
y = 4x - 5