there are 55 blades of grass and a 1 in.² of your lawn. There are 230 plates of grass in a 4 in.² of the same line. Write a linear equation in slope intercept form to model the situation

Calculate the slope $m$ of the line using the formula

m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{230 - 55}{4 - 1} = \frac{175}{3}.

Use the point-slope form of the equation:

y - y_1 = m(x - x_1).

Substitute $m = \frac{175}{3}$ and $(x_1, y_1) = (1, 55)$:

y - 55 = \frac{175}{3}(x - 1).

Expand and solve for $y$:

y - 55 = \frac{175}{3}x - \frac{175}{3}.

Add 55 to both sides:

y = \frac{175}{3}x - \frac{175}{3} + 55.

Convert 55 to a fraction with a denominator of 3:

55 = \frac{165}{3}.

Now combine the fractions:

y=\frac{175}{3}x+\frac{165}{3}-\frac{175}{3}=\frac{175}{3}x-\frac{10}{3}.

The linear equation in slope-intercept form is:

y=\frac{175}{3}x-\frac{10}{3}.

Answer: y=\frac{175}{3}x-\frac{10}{3}