(a) The linear equation is y=6−7x.

In a linear equation \(\displaystyle{y}={b}_{{0}}+{b}_{{1}}{x}\) the constant \(\displaystyle{b}_{{1}}\) be the slope and \(\displaystyle{b}_{{0}}\) be the y-intercept form and x is the independent variable and y is the independent variable.

Comparing the given equation with the general form of linear equation the slope of the equation is –7 and the y-intercept is 6.

Thus, the slope of the linear equation is \(\displaystyle{b}_{{1}}=−{7}\) and the y-intercept is \(\displaystyle{b}_{{0}}={6}\).

(b) In a linear equation \(\displaystyle{y}={b}_{{0}}+{b}_{{1}}{x}\) the constant \(\displaystyle{b}_{{1}}\) be the slope and \(\displaystyle{b}_{{0}}\) be the y-intercept form and x is the independent variable and y is the independent variable.

It is known that, the slope of the linear equation \(\displaystyle{y}={b}_{{0}}+{b}_{{1}}{x}\) is upward if \(\displaystyle{b}_{{1}}{>}{0}\), the slope of the linear equation \(\displaystyle{y}={b}_{{0}}+{b}_{{1}}{x}{y}={b}_{{0}}+{b}_{{1}}{x}\) is downward if \(\displaystyle{b}_{{1}}{<}{0}\) and the slope of the linear equation \(\displaystyle{y}={b}_{{0}}+{b}_{{1}}{x}\) is horizontal if \(\displaystyle{b}_{{1}}={0}.\)

Thus, in the given equation \(\displaystyle{y}={6}−{7}{x},{b}_{{1}}=−{7}{<}{0}.\)

Thus, the slope is downward.

(c) The linear equation is y=6−7x.

Graph the line:

The two points \(\displaystyle{\left({x}_{{1}}, {y}_{{1}}\right)}{\quad\text{and}\quad}{\left({x}_{{2}}, {y}_{{2}}\right)}\) on the given line are obtained:

If x = 0,

\(y=6+(−7 \times 0)\)

y=6

Thus, one point on the line is \(\displaystyle{\left({x}_{{1}}, {y}_{{1}}\right)}={\left({0},{6}\right)}.\)

If x = 1,

\(y=6+(−7 \times 1)\)

y=−1

Thus, the second point on the line is \(\displaystyle{\left({x}_{{2}}, {y}_{{2}}\right)}={\left({1},−{1}\right)}.\)