First, let's recall the point-slope form of a line equation: y - y1 = m(x - x1). This mathematical formula allows us to draw a line through a particular point (x1, y1) with a known slope.
Given that we have a point (2, 7) and the slope is 4/5, we can substitute these values into our formula. Therefore, we get y - 7 = 4/5 * (x - 2).
Now, we need to convert the equation to the slope-intercept form, which is y = mx + b. To do this, we need to distribute and simplify the equation. We'll start with the right side:
- Multiply 4/5 (the 'm' or slope value) with (x - 2), which yields (4/5)x - 8/5.
- After that, add '7' to both sides to get 'y' by itself.
Adding these two parts together, we get the equation y = (4/5)x - 8/5 + 7.
To simplify further, we have to convert the '7' to fifths. We know that 1 is equivalent to 5/5, so '7' is 35/5. Therefore, when we replace '7' with '35/5', the equation becomes y = (4/5)x - 8/5 + 35/5.
Finally, let's add the fractions together. We get y = (4/5)x + 27/5.
And there we have our slope-intercept form of the equation. When the slope is 4/5 and the line passes through the point (2,7), the equation of the line is y = (4/5)x + 27/5.